Simultaneous inference for Best Linear Predictor of the Conditional Average Treatment Effect and other structural functions

By Victor Chernozhukov, Vira Semenova. 2017

16 citations recorded by the source corpus.

This paper provides estimation and inference methods for a structural function, such as Conditional Average Treatment Effect (CATE), based on modern machine learning (ML) tools. We assume that such function can be represented as a conditional expectation = of a signal , where is the unknown nuisance function. In addition to CATE, examples of such functions include regression function with Partially Missing Outcome and Conditional Average Partial Derivative. We approximate by a linear form , where is a vector of the approximating functions and is the Best Linear Predictor. Plugging in the fi rst-stage estimate into the signal , we estimate via ordinary least squares of on . We deliver a high-quality estimate of the pseudo-target function , that features (a) a pointwise Gaussian approximation of at a point , (b) a simultaneous Gaussian approximation of uniformly over x, and (c) optimal rate of convergence of to uniformly over x. In the case the misspeci cation error of the linear form decays sufficiently fast, these approximations automatically hold for the target function instead of a pseudo-target . The fi rst stage nuisance parameter is allowed to be high-dimensional and is estimated by modern ML tools, such as neural networks, -shrinkage estimators, and random forest. Using our method, we estimate the average price elasticity conditional on income using Yatchew and No (2001) data and provide uniform con fidence bands for the target regression function.

Subfields: Economics and Econometrics, Statistics and Probability

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Citations in the corpus

Double/De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers (2018, methodology): “[2014]; Ning and Liu [2017]; Chernozhukov et al. [2015]; Neykov et al.”
Estimation of Conditional Average Treatment Effects With High-Dimensional Data (2019, methodology): “Third, we also provide a reasonably detailed discussion of the primitive conditions under which lasso estimation fulfills the high-level conditions posited in the article, while Chernozhukov and Semenova (2019) restricted attention to high-level analysis.”
Nonparametric estimation of causal heterogeneity under high-dimensional confounding (2019, background): “Recently, Chernozhukov and Semenova (2018) use their framework to estimate effect heterogeneity based on linear models. They provide conditions under which their second-stage linear model can become increasingly flexible. Postulating nonparametric second stages, we do not assume any specific functio”